Being "not the typical use case... in industry" doesn't make it bad. It just makes it a pure mathematics book. Formal theorem proving in vector spaces is the typical use case of a pure mathematician; this book is for them.
If you're looking to do application, use an applied book. Gilbert Strang's "Linear Algebra and its Applications" is quite good.
I'll second that. Strang's book is by far my favorite introductory math book. He addresses fundamentals quite well, and gives good treatment to applications such as linear programming and game theory.
If you're looking to do application, use an applied book. Gilbert Strang's "Linear Algebra and its Applications" is quite good.